Characterizations of the ∂-cohomology groups for a family of weakly pseudoconvex manifolds

Hideaki KAZAMA; Kwang Ho SHON

doi:10.2969/jmsj/03940685

Hideaki KAZAMA, Kwang Ho SHON

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 4 Pages 685-700

DOI https://doi.org/10.2969/jmsj/03940685

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Published: 1987 Received: May 24, 1986 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Publ. Math. IHES, 25 (1965), 81-130.
2) V. I. Arnold, Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves, Funkcional. Anal. i. Prilozen., 10 (1976), 1-12. (English translation, Functional Anal. Appl., 10 (1977), 249-259).
3) H. Grauert, über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
4) H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z., 81 (1963), 377-391.
5) L. Hörmander, An introduction to complex analysis in several variables, Van Nostrand, 1966.
6) H. Kazama, ∂ Cohomology of (H, C)-groups, Publ. RIMS, Kyoto Univ., 20 (1984), 297-317.
7) H. Kazama and K. H. Shon, ∂-Problem on a family of weakly pseudoconvex manifolds, Proc. Japan Acad., 62 (1986), 19-20.
8) H. Kazama and T. Umeno, Complex abelian Lie groups with finite-dimensional cohomology groups, J. Math. Soc. Japan, 36 (1984), 91-106.
9) J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds I. II., Ann. Math., 78 (1963), 112-148; ibid, 79 (1964), 450-472.
10) B. Malgrange, La cohomologie d'une variété analytique complexe à bord pseudoconvexen'est pas nécessairement séparée, C. R. Acad. Sci. Paris, 280 (1975), 93-95.
11) J. Morrow and K. Kodaira, Complex manifolds, Holt, Rinehart and Winston Inc., 1971.
12) T. Ueda, On the neighborhood of a compact complex curve with topologically trivial normal bundle, J. Math. Kyoto Univ., 22 (1983), 583-607.
13) C. Vogt, Line bundles on toroidal groups, J. Reine Angew. Math., 335 (1982), 197-215.
14) C. Vogt, Two remarks concerning toroidal groups, Manuscripta Math., 41 (1983), 217-232.

Right : [1] A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Publ. Math. IHES, 25 (1965), 81-130.
[2] V. I. Arnold, Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves, Funkcional. Anal. i. Prilozen., 10 (1976), 1-12. (English translation, Functional Anal. Appl., 10 (1977), 249-259).
[3] H. Grauert, über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), 331-368.
[4] H. Grauert, Bemerkenswerte pseudokonvexe Mannigfaltigkeiten, Math. Z., 81 (1963), 377-391.
[5] L. Hörmander, An introduction to complex analysis in several variables, Van Nostrand, 1966.
[6] H. Kazama, ∂ Cohomology of (H, C)-groups, Publ. RIMS, Kyoto Univ., 20 (1984), 297-317.
[7] H. Kazama and K. H. Shon, ∂-Problem on a family of weakly pseudoconvex manifolds, Proc. Japan Acad., 62 (1986), 19-20.
[8] H. Kazama and T. Umeno, Complex abelian Lie groups with finite-dimensional cohomology groups, J. Math. Soc. Japan, 36 (1984), 91-106.
[9] J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds I. II., Ann. Math., 78 (1963), 112-148; Ann. Math., 79 (1964), 450-472.
[10] B. Malgrange, La cohomologie d'une variété analytique complexe à bord pseudoconvexe n'est pas nécessairement séparée, C. R. Acad. Sci. Paris, 280 (1975), 93-95.
[11] J. Morrow and K. Kodaira, Complex manifolds, Holt, Rinehart and Winston Inc., 1971.
[12] T. Ueda, On the neighborhood of a compact complex curve with topologically trivial normal bundle, J. Math. Kyoto Univ., 22 (1983), 583-607.
[13] C. Vogt, Line bundles on toroidal groups, J. Reine Angew. Math., 335 (1982), 197-215.
[14] C. Vogt, Two remarks concerning toroidal groups, Manuscripta Math., 41 (1983), 217-232.

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